Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

Q: Q2. Solve the Bernoulli IVP, 1 x²y/ – 2xy = 3y*, y(1) = 2°

A: Solution of the differential equation

Q: Find the Particular solution of the ODE d²y dy - 62-7y = -9e-2x, at y(0) = -2 and ỹ(0) = –13 dx2 dx

A: To find The particular solution of the given ODE.

Q: Find the general solution of (D*+50D²+625) y =0̟ A y=c,cos5x + c,sin5x + c zxcos5x + c „rsin5x 5x Sx…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: 3. Determine the general solution. a) y"–2y' – 3y= e* b) y"+9y= cos x

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Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

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Q: Find the solution of x²y" +5xy' +(4+4x)y=0, x > 0 of the form n =1,2,3,... where co 1. Enter r = =…

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Q: Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,)…

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Q: The general solution of (D2-2D+ 1)y=2sin x A y=ce*+ c2xe*+2sinx B y=ce*+c2xe*+ cosx © y= ce*+ c2xe*…

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Q: Find the solution. (D3 +7D2 + 19D + 13)y =0; when x =0, y=0, y' =2, y"=-12 (A y = e*cosx B y =…

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Q: Find the General Solution of (D² + 5DD' +6D2)Z = 10 cos(x - y)

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Q: Find the general solution of the D.E (D^2+4)y=sin3x

A: We have to solve the problem

Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e*+C,cos2r + C ,sin2x c) none of the given…

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Q: d³y d²y, dy 4- + + 26 = x3 – 3 dx3 dx² dx

A: given differential equation isd3ydx3-4d2ydx2+dydx+26=x3-3for complemantry solution of given…

Q: Q4: Solve the following equation: d²y + 16y = cos²x %3D dx2 Using D-Operator method

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Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

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Q: Find the formulation of a particular solution of y"+2y'+ 5y = t² +4t – t²e-t cos 2t without…

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Q: 3. Find the general solutions of, (xy + x* )dy + y°dx = 0 b.

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Q: The general solution of y''+4y'= 0 is ° y = C, + C,x+ C,e* ° y = C,e* + C,e²* + C;e2* -4x y = C,e* +…

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Q: The general solution of (D3+4D)y 0 is y= e"(c,cos2x+c,sin2x) y=C+c2x+C3e ax B © y=c+c,cos2x+c3sin2x…

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Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: Q5 Find the General Solution of (D² + 5DD' + 6D²)Z = 10 cos(x – y)

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Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Q16// find the general solution (cosx)y²dx + 2ysinx dy = 0

A: I

Q: Find the General Solution of (D² + 5DD' + 6D²)Z = 10 cos(x – y)

A: Given partial differential equation is D2+5DD'+6D'2Z=10cosx−y. We have to find the general solution…

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: Find the solution. (D4 + 18D2 + 81)y = 0 A y = (c, + c,x)e²"cos3x + (c,+cx)e2'sin3x. y = (c, + c,)…

A: 16 Given differential equation is D4+18D2+81y=0 We have to find the general solution of the given…

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: Find the solution of xy" + 5xy +(4 – Ix)y = 0, x > 0 of the form where co = 1. Enter n= 1,2,3, ...

A: Let the solution of the above differential equation is given as: y=xr∑n=0∞cnxny=∑n=0∞cnxr+nThe…

Q: Show that the equation Əy 2 a3y + 2k possesses solutions of the form 00 -kt E C,e cos (C, x+ E,) cos…

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Q: The solution of the IVP x dx + 2ydy30, y(0)=2 is O None of these. x3 4- y3D x3 y=21 3. y=2,1+

A: Variable separable form : If the variable of the differential equation is separated then; Rewrite…

Q: Find the general equation solution to the 2Zx + Zy +Z = o

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Q: Find the general solution of the given DE. y"-2y"-y'+ 2y 0 %D

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is given by

Q: 3) a) Solve:' 4x³y +4x?y(2)_ sxy'+2y=0 Co,0) on

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Q: Find the general solution of (D4+ 50D2+ 625) y=0 (A y=c,cos5x + c,sin5x +czxcos5x + c „xsin5x B)…

A: Let's find.

Q: dy + ydx %3D = 3x²y?dx,

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Q: Find the solution. (D³ +7D2 + 19D + 13)y =0; when x =0, y=0. y' =2, y"=-12 A y = e-2'sin3x B y =…

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Q: Find the General Solution (D² – 3D + 2)y = cos(e¬*)

A: We need to find the general solution of (D2-3D+2)y=cos(e-x) Note the results  ∫cosx dx=sinx+C ∫sinx…

Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: The general solution of (D³+4D)y=0 is A y=ce*+c2ex+ C3e=2x B y=c+c2x+cze¬4x y=c1+C2x+C3e- B ©…

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D. Answer:

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Q: y" + 3y' + 2y - 10e + 4x²

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Q: Find the general solution of (D² + 5DD' + 6D²)Z = 10 cos(2x + 5y).

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Q: Find the general solution of (D4+50D²+ 625) y=0 A y=c,cos5x+c „sin5x y=c,cos5x+c,sin5x + c zxcos5x+c…

A: Answer: option C is correct answer To find: general solution.

Q: Find the general solution of D² + 16D)y = cos4x

A: We have to find general solution of the differential equation: D2+16Dy=cos4x Auxiliary equation…